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Puzzle 479: Polyominous 44

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term said...

Have I mentioned recently how much I like the little bits of unexpected logic you save for the very end?

Grant Fikes said...

Term: What does that have to do with this puzzle? :)

Anonymous said...

good puzzle :)

Linda, VP Puzzles said...

Do you make all of these by-hand, or use software to help you? I'm wondering how hard it would be to code polyominous puzzles.

Grant Fikes said...

Linda: All of the Polyominous puzzles on this blog are crafted by hand. I currently know of two sources of computer-generated Fillomino puzzles. Simon Tatham's applet generates puzzles on the fly of any size the user specifies, but makes no attempt to arrange the givens symmetrically (a feat which a human can accomplish very easily), makes no effective use of the rule that no two polyominoes of the same size can share an edge, and almost never uses "implied" polyominoes which contain none of the givens (I think I've seen an implied monomino once in a few dozen puzzles, but that's it). Vegard Hanssen's site offers pre-generated 5x5 and 7x7 puzzles only, but at least offers both "optimal" puzzles and "symmetrical" puzzles. In my personal opinion, though, none of these computer-generated puzzles offer the same artisanship which handmade ones do.

When a computer algorithm comes along capable of making Fillomino puzzles with the same artisanship as this puzzle, this puzzle, this puzzle, this puzzle, or this puzzle, let me know.

Grant Fikes said...

An update: I did some investigation involving the Game->Specific and Game->Solve functions of Tatham's applet.

2x3:030200 and 3x3:303003020 can be solved.
2x3:030100, 4x2:00401022, 7x2:60000060002000, and 9x4:020149007200040000000040007900147070 cannot be solved.

I think the program only knows two techniques: a) for the number n at cell x to be part of a region of exactly n cells, these cells must also have the number n, and b) this single cell is surrounded by completed regions, and is therefore 1. This prevents it from generating truly deep Fillomino puzzles. The thing is that a truly beautiful Fillomino, like many puzzles, must balance depth and doability. If an algorithm is too deep, it will be able to solve and generate puzzles which require too much wearisome trial and error for a human to enjoy. If an algorithm is too shallow, the puzzles are solvable, but flavorless. I believe a human is better able to determine what a human will enjoy solving than a computer, and much more capable of the artistic creativity which makes puzzles such as the five I mentioned in my previous comment possible.

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